Towards parametrizing word equations

@article{Abdulrab2010,
abstract = { Classically, in order to resolve an equation u ≈ v over a free monoid X*, we reduce it by a suitable family $\cal F$ of substitutions to a family of equations uf ≈ vf, $f\in\cal F$, each involving less variables than u ≈ v, and then combine solutions of uf ≈ vf into solutions of u ≈ v. The problem is to get $\cal F$ in a handy parametrized form. The method we propose consists in parametrizing the path traces in the so called graph of prime equations associated to u ≈ v. We carry out such a parametrization in the case the prime equations in the graph involve at most three variables. },
author = {Abdulrab, H., Goralčík, P., Makanin, G. S.},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Equation; free monoid; parametrization; universal family.; universal family},
language = {eng},
month = {3},
number = {4},
pages = {331-350},
publisher = {EDP Sciences},
title = {Towards parametrizing word equations},
url = {http://eudml.org/doc/222084},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Abdulrab, H.
AU - Goralčík, P.
AU - Makanin, G. S.
TI - Towards parametrizing word equations
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 4
SP - 331
EP - 350
AB - Classically, in order to resolve an equation u ≈ v over a free monoid X*, we reduce it by a suitable family $\cal F$ of substitutions to a family of equations uf ≈ vf, $f\in\cal F$, each involving less variables than u ≈ v, and then combine solutions of uf ≈ vf into solutions of u ≈ v. The problem is to get $\cal F$ in a handy parametrized form. The method we propose consists in parametrizing the path traces in the so called graph of prime equations associated to u ≈ v. We carry out such a parametrization in the case the prime equations in the graph involve at most three variables.
LA - eng
KW - Equation; free monoid; parametrization; universal family.; universal family
UR - http://eudml.org/doc/222084
ER -